复标量场厚膜：线性扰动的稳定性及与引力耦合的标量Kaluza-Klein模式的演化
Complex scalar field thick branes: stability of linear perturbation and evolution of scalar Kaluza-Klein modes coupled with gravity
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- School of Physics, Xidian University（西安电子科技大学物理学院）
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中文总结 AI 辅助
本文研究复标量场厚膜的稳定性与局域化，发现标量、矢量、张量扰动均稳定，且标量KK模式在Minkowski和dS膜上连续、在AdS膜上离散，共振随参数$\beta$增强而增多。
中文摘要 AI 辅助
我们研究了由复标量场$\Phi$产生的Minkowski、de Sitter (dS)和anti-de Sitter (AdS)厚膜的稳定性与局域化性质。标量自相互作用势包含一个温度参数$a$。当$a$接近其临界值时，$\Phi$的虚部变为双扭结形，能量密度分裂为两个峰，表明形成了两个子膜。对标量、矢量和张量线性扰动的分析显示，标量和矢量扇区没有不稳定的迹象，而张量扰动方程的可分解性排除了快子张量模式。引力子零模局域在Minkowski和dS膜上，但在AdS膜上不可归一化。我们进一步研究了一个实测试标量场$\Psi$，其动能项与时空曲率之间存在耦合函数$F(R)$。标量零模总能局域在Minkowski和dS膜上，并具有连续的、无间隙的标量Kaluza-Klein (KK)模式谱。对于合适的$\beta$值，在$a$的临界值附近会出现有质量标量共振。增大$\beta$会产生更多共振，并延长较低共振的寿命，而它们的时间演化表现出亚稳态模式的典型衰变特征。对于AdS膜，标量零模也是局域的，而边界处发散的有效势将有质量标量KK模式束缚为束缚态，从而产生离散的质量谱。
英文摘要
We investigate the stability and localization properties of Minkowski, de Sitter (dS), and anti-de Sitter (AdS) thick branes generated by a complex scalar field $Φ$. The scalar self-interaction potential contains a temperature parameter $a$. As $a$ approaches its critical value, the imaginary part of $Φ$ becomes double-kinked and the energy density splits into two peaks, indicating the formation of two sub-branes. The analysis of linear scalar, vector, and tensor perturbations shows no signs of instability in the scalar and vector sectors, while the factorization of the tensor perturbation equation excludes tachyonic tensor modes. The graviton zero mode is localized on the Minkowski and dS branes but is not normalizable on the AdS brane. We further study a real test scalar field $Ψ$ with a coupling function $F(R)$ between its kinetic term and the spacetime curvature. The scalar zero mode can always be localized on the Minkowski and dS branes, with a continuous gapless spectrum of scalar Kaluza--Klein (KK) modes. Massive scalar resonances emerge near the critical value of $a$ for suitable values of $β$. Increasing $β$ produces more resonances and prolongs the lifetimes of the lower resonances, while their time evolution exhibits the characteristic decay of metastable modes. For the AdS brane, the scalar zero mode is also localized, whereas the divergent effective potential at the boundaries traps the massive scalar KK modes as bound states, yielding a discrete mass spectrum.
